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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DD correctly emulated by HHH --- Totally ignoring invalid
 rebuttals ---PSR---
Date: Sat, 8 Mar 2025 19:56:31 -0500
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On 3/8/2025 7:29 PM, olcott wrote:
> On 3/8/2025 5:31 PM, dbush wrote:
>> On 3/8/2025 6:23 PM, olcott wrote:
>>> On 3/8/2025 4:58 PM, dbush wrote:
>>>> On 3/8/2025 5:42 PM, olcott wrote:
>>>>> On 3/8/2025 9:00 AM, dbush wrote:
>>>>>> On 3/8/2025 9:03 AM, olcott wrote:
>>>>>>>
>>>>>>> Apparently you don't understand that inputs to a
>>>>>>> simulating termination analyzer specifying infinite
>>>>>>> recursion or recursive emulation cannot possibly
>>>>>>> reach their own final state and terminate normally.
>>>>>>
>>>>>> Apparently you don't understand that inputs to a termination 
>>>>>> analyzer, simulating or otherwise, are specified by the 
>>>>>> specification that is the halting function:
>>>>>>
>>>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
>>>>>>
>>>>>> And HHH(DD)==0 fails to meet the above specification
>>>>>
>>>>> *THIS IS A SEMANTIC TAUTOLOGY THUS IMPOSSIBLY FALSE*
>>>>> Replacing the code of HHH with an unconditional simulator and 
>>>>> subsequently running HHH(DD) cannot possibly reach
>>>>> its own "ret" instruction and terminate normally
>>>>> because DD calls HHH(DD) in recursive emulation.
>>>>>
>>>>> It is ridiculously stupid to believe that HHH must
>>>>> report on behavior other than the above behavior.
>>>>>
>>>>
>>>> It must if it is to be classified as a halt decider or termination 
>>>> analyzer as per the definition.
>>>
>>> In other words you believe that HHH 
>>
>> Is required to map the halting function to meet the requirements to be 
>> a halt decider / termination analyzer.
>>
> 
> HHH must map from the input finite string DD
> to the behavior that this finite string specifies

And what it specifies, to be considered a solution to the halting 
problem, is given by the specification:

Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
described as <X> with input Y:

A solution to the halting problem is an algorithm H that computes the 
following mapping:

(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed